LMFDB - Embedded newform 7935.2.a.bt.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,1,-25,31,-25,-1,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.185184 q^{2} -1.00000 q^{3} -1.96571 q^{4} -1.00000 q^{5} -0.185184 q^{6} +4.18574 q^{7} -0.734387 q^{8} +1.00000 q^{9} -0.185184 q^{10} +2.22165 q^{11} +1.96571 q^{12} +2.71080 q^{13} +0.775133 q^{14} +1.00000 q^{15} +3.79542 q^{16} -4.35172 q^{17} +0.185184 q^{18} +6.68852 q^{19} +1.96571 q^{20} -4.18574 q^{21} +0.411415 q^{22} +0.734387 q^{24} +1.00000 q^{25} +0.501998 q^{26} -1.00000 q^{27} -8.22793 q^{28} +5.07981 q^{29} +0.185184 q^{30} +2.45676 q^{31} +2.17163 q^{32} -2.22165 q^{33} -0.805871 q^{34} -4.18574 q^{35} -1.96571 q^{36} +5.28265 q^{37} +1.23861 q^{38} -2.71080 q^{39} +0.734387 q^{40} -5.40047 q^{41} -0.775133 q^{42} +10.6778 q^{43} -4.36711 q^{44} -1.00000 q^{45} -2.26733 q^{47} -3.79542 q^{48} +10.5204 q^{49} +0.185184 q^{50} +4.35172 q^{51} -5.32864 q^{52} +13.4418 q^{53} -0.185184 q^{54} -2.22165 q^{55} -3.07395 q^{56} -6.68852 q^{57} +0.940702 q^{58} +6.09520 q^{59} -1.96571 q^{60} +4.75583 q^{61} +0.454955 q^{62} +4.18574 q^{63} -7.18868 q^{64} -2.71080 q^{65} -0.411415 q^{66} +10.5564 q^{67} +8.55421 q^{68} -0.775133 q^{70} -10.3824 q^{71} -0.734387 q^{72} -5.07163 q^{73} +0.978264 q^{74} -1.00000 q^{75} -13.1477 q^{76} +9.29924 q^{77} -0.501998 q^{78} -9.20725 q^{79} -3.79542 q^{80} +1.00000 q^{81} -1.00008 q^{82} -8.87707 q^{83} +8.22793 q^{84} +4.35172 q^{85} +1.97736 q^{86} -5.07981 q^{87} -1.63155 q^{88} +0.783796 q^{89} -0.185184 q^{90} +11.3467 q^{91} -2.45676 q^{93} -0.419874 q^{94} -6.68852 q^{95} -2.17163 q^{96} -1.06264 q^{97} +1.94821 q^{98} +2.22165 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.185184	0.130945	0.0654726	−	0.997854i	$-0.479145\pi$
$2$	0.185184	0.130945	0.0654726	+	0.997854i	$0.479145\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96571	−0.982853
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.185184	−0.0756012
$7$	4.18574	1.58206	0.791030	−	0.611778i	$-0.209545\pi$
$7$	4.18574	1.58206	0.791030	+	0.611778i	$0.209545\pi$
$8$	−0.734387	−0.259645
$9$	1.00000	0.333333
$10$	−0.185184	−0.0585605
$11$	2.22165	0.669853	0.334926	−	0.942244i	$-0.391289\pi$
$11$	2.22165	0.669853	0.334926	+	0.942244i	$0.391289\pi$
$12$	1.96571	0.567451
$13$	2.71080	0.751841	0.375920	−	0.926652i	$-0.377327\pi$
$13$	2.71080	0.751841	0.375920	+	0.926652i	$0.377327\pi$
$14$	0.775133	0.207163
$15$	1.00000	0.258199
$16$	3.79542	0.948854
$17$	−4.35172	−1.05545	−0.527724	−	0.849416i	$-0.676954\pi$
$17$	−4.35172	−1.05545	−0.527724	+	0.849416i	$0.676954\pi$
$18$	0.185184	0.0436484
$19$	6.68852	1.53445	0.767226	−	0.641376i	$-0.221636\pi$
$19$	6.68852	1.53445	0.767226	+	0.641376i	$0.221636\pi$
$20$	1.96571	0.439545
$21$	−4.18574	−0.913403
$22$	0.411415	0.0877140
$23$	0	0
$23$	0	0
$24$	0.734387	0.149906
$25$	1.00000	0.200000
$26$	0.501998	0.0984499
$27$	−1.00000	−0.192450
$28$	−8.22793	−1.55493
$29$	5.07981	0.943297	0.471648	−	0.881787i	$-0.343659\pi$
$29$	5.07981	0.943297	0.471648	+	0.881787i	$0.343659\pi$
$30$	0.185184	0.0338099
$31$	2.45676	0.441248	0.220624	−	0.975359i	$-0.429191\pi$
$31$	2.45676	0.441248	0.220624	+	0.975359i	$0.429191\pi$
$32$	2.17163	0.383893
$33$	−2.22165	−0.386740
$34$	−0.805871	−0.138206
$35$	−4.18574	−0.707519
$36$	−1.96571	−0.327618
$37$	5.28265	0.868462	0.434231	−	0.900802i	$-0.357020\pi$
$37$	5.28265	0.868462	0.434231	+	0.900802i	$0.357020\pi$
$38$	1.23861	0.200929
$39$	−2.71080	−0.434075
$40$	0.734387	0.116117
$41$	−5.40047	−0.843412	−0.421706	−	0.906733i	$-0.638569\pi$
$41$	−5.40047	−0.843412	−0.421706	+	0.906733i	$0.638569\pi$
$42$	−0.775133	−0.119606
$43$	10.6778	1.62835	0.814174	−	0.580620i	$-0.197190\pi$
$43$	10.6778	1.62835	0.814174	+	0.580620i	$0.197190\pi$
$44$	−4.36711	−0.658367
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−2.26733	−0.330724	−0.165362	−	0.986233i	$-0.552879\pi$
$47$	−2.26733	−0.330724	−0.165362	+	0.986233i	$0.552879\pi$
$48$	−3.79542	−0.547821
$49$	10.5204	1.50291
$50$	0.185184	0.0261890
$51$	4.35172	0.609363
$52$	−5.32864	−0.738949
$53$	13.4418	1.84637	0.923185	−	0.384357i	$-0.125577\pi$
$53$	13.4418	1.84637	0.923185	+	0.384357i	$0.125577\pi$
$54$	−0.185184	−0.0252004
$55$	−2.22165	−0.299567
$56$	−3.07395	−0.410774
$57$	−6.68852	−0.885917
$58$	0.940702	0.123520
$59$	6.09520	0.793527	0.396764	−	0.917921i	$-0.370133\pi$
$59$	6.09520	0.793527	0.396764	+	0.917921i	$0.370133\pi$
$60$	−1.96571	−0.253772
$61$	4.75583	0.608921	0.304461	−	0.952525i	$-0.401524\pi$
$61$	4.75583	0.608921	0.304461	+	0.952525i	$0.401524\pi$
$62$	0.454955	0.0577793
$63$	4.18574	0.527353
$64$	−7.18868	−0.898585
$65$	−2.71080	−0.336233
$66$	−0.411415	−0.0506417
$67$	10.5564	1.28967	0.644835	−	0.764322i	$-0.276926\pi$
$67$	10.5564	1.28967	0.644835	+	0.764322i	$0.276926\pi$
$68$	8.55421	1.03735
$69$	0	0
$70$	−0.775133	−0.0926461
$71$	−10.3824	−1.23216	−0.616081	−	0.787683i	$-0.711281\pi$
$71$	−10.3824	−1.23216	−0.616081	+	0.787683i	$0.711281\pi$
$72$	−0.734387	−0.0865484
$73$	−5.07163	−0.593590	−0.296795	−	0.954941i	$-0.595918\pi$
$73$	−5.07163	−0.593590	−0.296795	+	0.954941i	$0.595918\pi$
$74$	0.978264	0.113721
$75$	−1.00000	−0.115470
$76$	−13.1477	−1.50814
$77$	9.29924	1.05975
$78$	−0.501998	−0.0568401
$79$	−9.20725	−1.03590	−0.517948	−	0.855412i	$-0.673304\pi$
$79$	−9.20725	−1.03590	−0.517948	+	0.855412i	$0.673304\pi$
$80$	−3.79542	−0.424340
$81$	1.00000	0.111111
$82$	−1.00008	−0.110441
$83$	−8.87707	−0.974385	−0.487192	−	0.873295i	$-0.661979\pi$
$83$	−8.87707	−0.974385	−0.487192	+	0.873295i	$0.661979\pi$
$84$	8.22793	0.897741
$85$	4.35172	0.472010
$86$	1.97736	0.213224
$87$	−5.07981	−0.544613
$88$	−1.63155	−0.173924
$89$	0.783796	0.0830822	0.0415411	−	0.999137i	$-0.486773\pi$
$89$	0.783796	0.0830822	0.0415411	+	0.999137i	$0.486773\pi$
$90$	−0.185184	−0.0195202
$91$	11.3467	1.18946
$92$	0	0
$93$	−2.45676	−0.254755
$94$	−0.419874	−0.0433067
$95$	−6.68852	−0.686228
$96$	−2.17163	−0.221641
$97$	−1.06264	−0.107895	−0.0539474	−	0.998544i	$-0.517180\pi$
$97$	−1.06264	−0.107895	−0.0539474	+	0.998544i	$0.517180\pi$
$98$	1.94821	0.196799
$99$	2.22165	0.223284
$100$	−1.96571	−0.196571
$101$	−11.7380	−1.16798	−0.583988	−	0.811762i	$-0.698508\pi$
$101$	−11.7380	−1.16798	−0.583988	+	0.811762i	$0.698508\pi$
$102$	0.805871	0.0797931
$103$	12.3240	1.21432	0.607162	−	0.794578i	$-0.292308\pi$
$103$	12.3240	1.21432	0.607162	+	0.794578i	$0.292308\pi$
$104$	−1.99078	−0.195212
$105$	4.18574	0.408486
$106$	2.48921	0.241773
$107$	−5.96673	−0.576826	−0.288413	−	0.957506i	$-0.593128\pi$
$107$	−5.96673	−0.576826	−0.288413	+	0.957506i	$0.593128\pi$
$108$	1.96571	0.189150
$109$	−2.83780	−0.271812	−0.135906	−	0.990722i	$-0.543395\pi$
$109$	−2.83780	−0.271812	−0.135906	+	0.990722i	$0.543395\pi$
$110$	−0.411415	−0.0392269
$111$	−5.28265	−0.501407
$112$	15.8866	1.50114
$113$	−16.6051	−1.56208	−0.781038	−	0.624483i	$-0.785310\pi$
$113$	−16.6051	−1.56208	−0.781038	+	0.624483i	$0.785310\pi$
$114$	−1.23861	−0.116007
$115$	0	0
$116$	−9.98541	−0.927122
$117$	2.71080	0.250614
$118$	1.12874	0.103909
$119$	−18.2152	−1.66978
$120$	−0.734387	−0.0670401
$121$	−6.06427	−0.551298
$122$	0.880705	0.0797353
$123$	5.40047	0.486944
$124$	−4.82928	−0.433682
$125$	−1.00000	−0.0894427
$126$	0.775133	0.0690544
$127$	−3.48413	−0.309167	−0.154583	−	0.987980i	$-0.549404\pi$
$127$	−3.48413	−0.309167	−0.154583	+	0.987980i	$0.549404\pi$
$128$	−5.67449	−0.501558
$129$	−10.6778	−0.940128
$130$	−0.501998	−0.0440281
$131$	7.61728	0.665525	0.332763	−	0.943011i	$-0.392019\pi$
$131$	7.61728	0.665525	0.332763	+	0.943011i	$0.392019\pi$
$132$	4.36711	0.380108
$133$	27.9964	2.42760
$134$	1.95488	0.168876
$135$	1.00000	0.0860663
$136$	3.19585	0.274042
$137$	−19.1958	−1.64001	−0.820004	−	0.572358i	$-0.806029\pi$
$137$	−19.1958	−1.64001	−0.820004	+	0.572358i	$0.806029\pi$
$138$	0	0
$139$	−5.85394	−0.496525	−0.248262	−	0.968693i	$-0.579860\pi$
$139$	−5.85394	−0.496525	−0.248262	+	0.968693i	$0.579860\pi$
$140$	8.22793	0.695387
$141$	2.26733	0.190944
$142$	−1.92266	−0.161346
$143$	6.02245	0.503622
$144$	3.79542	0.316285
$145$	−5.07981	−0.421855
$146$	−0.939188	−0.0777277
$147$	−10.5204	−0.867707
$148$	−10.3841	−0.853571
$149$	−10.8501	−0.888871	−0.444436	−	0.895811i	$-0.646596\pi$
$149$	−10.8501	−0.888871	−0.444436	+	0.895811i	$0.646596\pi$
$150$	−0.185184	−0.0151202
$151$	−2.84135	−0.231226	−0.115613	−	0.993294i	$-0.536883\pi$
$151$	−2.84135	−0.231226	−0.115613	+	0.993294i	$0.536883\pi$
$152$	−4.91197	−0.398413
$153$	−4.35172	−0.351816
$154$	1.72207	0.138769
$155$	−2.45676	−0.197332
$156$	5.32864	0.426632
$157$	−21.9832	−1.75445	−0.877226	−	0.480078i	$-0.840609\pi$
$157$	−21.9832	−1.75445	−0.877226	+	0.480078i	$0.840609\pi$
$158$	−1.70504	−0.135646
$159$	−13.4418	−1.06600
$160$	−2.17163	−0.171682
$161$	0	0
$162$	0.185184	0.0145495
$163$	−0.0938907	−0.00735409	−0.00367704	−	0.999993i	$-0.501170\pi$
$163$	−0.0938907	−0.00735409	−0.00367704	+	0.999993i	$0.501170\pi$
$164$	10.6157	0.828950
$165$	2.22165	0.172955
$166$	−1.64389	−0.127591
$167$	3.53996	0.273930	0.136965	−	0.990576i	$-0.456265\pi$
$167$	3.53996	0.273930	0.136965	+	0.990576i	$0.456265\pi$
$168$	3.07395	0.237160
$169$	−5.65156	−0.434736
$170$	0.805871	0.0618075
$171$	6.68852	0.511484
$172$	−20.9894	−1.60043
$173$	5.83761	0.443825	0.221913	−	0.975067i	$-0.428770\pi$
$173$	5.83761	0.443825	0.221913	+	0.975067i	$0.428770\pi$
$174$	−0.940702	−0.0713144
$175$	4.18574	0.316412
$176$	8.43208	0.635592
$177$	−6.09520	−0.458143
$178$	0.145147	0.0108792
$179$	24.9111	1.86195	0.930973	−	0.365088i	$-0.118961\pi$
$179$	24.9111	1.86195	0.930973	+	0.365088i	$0.118961\pi$
$180$	1.96571	0.146515
$181$	26.2828	1.95358	0.976792	−	0.214189i	$-0.0687108\pi$
$181$	26.2828	1.95358	0.976792	+	0.214189i	$0.0687108\pi$
$182$	2.10123	0.155754
$183$	−4.75583	−0.351561
$184$	0	0
$185$	−5.28265	−0.388388
$186$	−0.454955	−0.0333589
$187$	−9.66800	−0.706994
$188$	4.45690	0.325053
$189$	−4.18574	−0.304468
$190$	−1.23861	−0.0898583
$191$	12.0022	0.868448	0.434224	−	0.900805i	$-0.357023\pi$
$191$	12.0022	0.868448	0.434224	+	0.900805i	$0.357023\pi$
$192$	7.18868	0.518798
$193$	−0.355524	−0.0255912	−0.0127956	−	0.999918i	$-0.504073\pi$
$193$	−0.355524	−0.0255912	−0.0127956	+	0.999918i	$0.504073\pi$
$194$	−0.196785	−0.0141283
$195$	2.71080	0.194124
$196$	−20.6800	−1.47714
$197$	14.0729	1.00265	0.501326	−	0.865259i	$-0.332846\pi$
$197$	14.0729	1.00265	0.501326	+	0.865259i	$0.332846\pi$
$198$	0.411415	0.0292380
$199$	−22.0154	−1.56063	−0.780314	−	0.625388i	$-0.784941\pi$
$199$	−22.0154	−1.56063	−0.780314	+	0.625388i	$0.784941\pi$
$200$	−0.734387	−0.0519290
$201$	−10.5564	−0.744592
$202$	−2.17370	−0.152941
$203$	21.2627	1.49235
$204$	−8.55421	−0.598914
$205$	5.40047	0.377185
$206$	2.28222	0.159010
$207$	0	0
$208$	10.2886	0.713387
$209$	14.8596	1.02786
$210$	0.775133	0.0534893
$211$	5.59537	0.385201	0.192601	−	0.981277i	$-0.438308\pi$
$211$	5.59537	0.385201	0.192601	+	0.981277i	$0.438308\pi$
$212$	−26.4226	−1.81471
$213$	10.3824	0.711389
$214$	−1.10495	−0.0755326
$215$	−10.6778	−0.728220
$216$	0.734387	0.0499687
$217$	10.2834	0.698080
$218$	−0.525517	−0.0355925
$219$	5.07163	0.342709
$220$	4.36711	0.294431
$221$	−11.7966	−0.793528
$222$	−0.978264	−0.0656568
$223$	15.7581	1.05524	0.527619	−	0.849481i	$-0.323085\pi$
$223$	15.7581	1.05524	0.527619	+	0.849481i	$0.323085\pi$
$224$	9.08986	0.607342
$225$	1.00000	0.0666667
$226$	−3.07501	−0.204546
$227$	2.05413	0.136337	0.0681686	−	0.997674i	$-0.478284\pi$
$227$	2.05413	0.136337	0.0681686	+	0.997674i	$0.478284\pi$
$228$	13.1477	0.870726
$229$	28.5833	1.88884	0.944418	−	0.328747i	$-0.106626\pi$
$229$	28.5833	1.88884	0.944418	+	0.328747i	$0.106626\pi$
$230$	0	0
$231$	−9.29924	−0.611845
$232$	−3.73055	−0.244922
$233$	−1.70186	−0.111492	−0.0557462	−	0.998445i	$-0.517754\pi$
$233$	−1.70186	−0.111492	−0.0557462	+	0.998445i	$0.517754\pi$
$234$	0.501998	0.0328166
$235$	2.26733	0.147904
$236$	−11.9814	−0.779921
$237$	9.20725	0.598075
$238$	−3.37316	−0.218650
$239$	13.8543	0.896158	0.448079	−	0.893994i	$-0.352108\pi$
$239$	13.8543	0.896158	0.448079	+	0.893994i	$0.352108\pi$
$240$	3.79542	0.244993
$241$	−6.50047	−0.418732	−0.209366	−	0.977837i	$-0.567140\pi$
$241$	−6.50047	−0.418732	−0.209366	+	0.977837i	$0.567140\pi$
$242$	−1.12301	−0.0721898
$243$	−1.00000	−0.0641500
$244$	−9.34856	−0.598480
$245$	−10.5204	−0.672123
$246$	1.00008	0.0637630
$247$	18.1313	1.15366
$248$	−1.80422	−0.114568
$249$	8.87707	0.562561
$250$	−0.185184	−0.0117121
$251$	11.2061	0.707323	0.353662	−	0.935373i	$-0.384936\pi$
$251$	11.2061	0.707323	0.353662	+	0.935373i	$0.384936\pi$
$252$	−8.22793	−0.518311
$253$	0	0
$254$	−0.645208	−0.0404839
$255$	−4.35172	−0.272515
$256$	13.3265	0.832909
$257$	20.4377	1.27487	0.637433	−	0.770506i	$-0.279996\pi$
$257$	20.4377	1.27487	0.637433	+	0.770506i	$0.279996\pi$
$258$	−1.97736	−0.123105
$259$	22.1118	1.37396
$260$	5.32864	0.330468
$261$	5.07981	0.314432
$262$	1.41060	0.0871473
$263$	28.1070	1.73315	0.866577	−	0.499043i	$-0.166315\pi$
$263$	28.1070	1.73315	0.866577	+	0.499043i	$0.166315\pi$
$264$	1.63155	0.100415
$265$	−13.4418	−0.825722
$266$	5.18450	0.317882
$267$	−0.783796	−0.0479675
$268$	−20.7508	−1.26756
$269$	−13.0359	−0.794812	−0.397406	−	0.917643i	$-0.630090\pi$
$269$	−13.0359	−0.794812	−0.397406	+	0.917643i	$0.630090\pi$
$270$	0.185184	0.0112700
$271$	30.6188	1.85996	0.929981	−	0.367607i	$-0.119823\pi$
$271$	30.6188	1.85996	0.929981	+	0.367607i	$0.119823\pi$
$272$	−16.5166	−1.00147
$273$	−11.3467	−0.686733
$274$	−3.55476	−0.214751
$275$	2.22165	0.133971
$276$	0	0
$277$	−29.7377	−1.78677	−0.893383	−	0.449296i	$-0.851675\pi$
$277$	−29.7377	−1.78677	−0.893383	+	0.449296i	$0.851675\pi$
$278$	−1.08406	−0.0650175
$279$	2.45676	0.147083
$280$	3.07395	0.183704
$281$	−19.1168	−1.14041	−0.570207	−	0.821501i	$-0.693137\pi$
$281$	−19.1168	−1.14041	−0.570207	+	0.821501i	$0.693137\pi$
$282$	0.419874	0.0250031
$283$	1.32401	0.0787045	0.0393522	−	0.999225i	$-0.487471\pi$
$283$	1.32401	0.0787045	0.0393522	+	0.999225i	$0.487471\pi$
$284$	20.4087	1.21103
$285$	6.68852	0.396194
$286$	1.11526	0.0659469
$287$	−22.6050	−1.33433
$288$	2.17163	0.127964
$289$	1.93747	0.113969
$290$	−0.940702	−0.0552399
$291$	1.06264	0.0622931
$292$	9.96934	0.583412
$293$	−3.27151	−0.191123	−0.0955617	−	0.995424i	$-0.530465\pi$
$293$	−3.27151	−0.191123	−0.0955617	+	0.995424i	$0.530465\pi$
$294$	−1.94821	−0.113622
$295$	−6.09520	−0.354876
$296$	−3.87951	−0.225492
$297$	−2.22165	−0.128913
$298$	−2.00926	−0.116393
$299$	0	0
$300$	1.96571	0.113490
$301$	44.6944	2.57615
$302$	−0.526174	−0.0302779
$303$	11.7380	0.674331
$304$	25.3857	1.45597
$305$	−4.75583	−0.272318
$306$	−0.805871	−0.0460686
$307$	4.27054	0.243733	0.121866	−	0.992547i	$-0.461112\pi$
$307$	4.27054	0.243733	0.121866	+	0.992547i	$0.461112\pi$
$308$	−18.2796	−1.04158
$309$	−12.3240	−0.701090
$310$	−0.454955	−0.0258397
$311$	26.8800	1.52423	0.762113	−	0.647445i	$-0.224162\pi$
$311$	26.8800	1.52423	0.762113	+	0.647445i	$0.224162\pi$
$312$	1.99078	0.112706
$313$	16.4712	0.931010	0.465505	−	0.885045i	$-0.345873\pi$
$313$	16.4712	0.931010	0.465505	+	0.885045i	$0.345873\pi$
$314$	−4.07095	−0.229737
$315$	−4.18574	−0.235840
$316$	18.0987	1.01813
$317$	9.83672	0.552485	0.276242	−	0.961088i	$-0.410911\pi$
$317$	9.83672	0.552485	0.276242	+	0.961088i	$0.410911\pi$
$318$	−2.48921	−0.139588
$319$	11.2856	0.631870
$320$	7.18868	0.401859
$321$	5.96673	0.333031
$322$	0	0
$323$	−29.1066	−1.61953
$324$	−1.96571	−0.109206
$325$	2.71080	0.150368
$326$	−0.0173871	−0.000962982 0
$327$	2.83780	0.156931
$328$	3.96604	0.218988
$329$	−9.49044	−0.523225
$330$	0.411415	0.0226476
$331$	−4.36076	−0.239689	−0.119844	−	0.992793i	$-0.538240\pi$
$331$	−4.36076	−0.239689	−0.119844	+	0.992793i	$0.538240\pi$
$332$	17.4497	0.957677
$333$	5.28265	0.289487
$334$	0.655545	0.0358698
$335$	−10.5564	−0.576758
$336$	−15.8866	−0.866686
$337$	−11.5975	−0.631758	−0.315879	−	0.948800i	$-0.602299\pi$
$337$	−11.5975	−0.631758	−0.315879	+	0.948800i	$0.602299\pi$
$338$	−1.04658	−0.0569265
$339$	16.6051	0.901865
$340$	−8.55421	−0.463917
$341$	5.45807	0.295571
$342$	1.23861	0.0669764
$343$	14.7354	0.795638
$344$	−7.84164	−0.422793
$345$	0	0
$346$	1.08104	0.0581168
$347$	−19.9381	−1.07033	−0.535166	−	0.844747i	$-0.679751\pi$
$347$	−19.9381	−1.07033	−0.535166	+	0.844747i	$0.679751\pi$
$348$	9.98541	0.535274
$349$	−15.8880	−0.850466	−0.425233	−	0.905084i	$-0.639808\pi$
$349$	−15.8880	−0.850466	−0.425233	+	0.905084i	$0.639808\pi$
$350$	0.775133	0.0414326
$351$	−2.71080	−0.144692
$352$	4.82459	0.257152
$353$	19.6009	1.04325	0.521625	−	0.853175i	$-0.325326\pi$
$353$	19.6009	1.04325	0.521625	+	0.853175i	$0.325326\pi$
$354$	−1.12874	−0.0599917
$355$	10.3824	0.551040
$356$	−1.54071	−0.0816576
$357$	18.2152	0.964048
$358$	4.61316	0.243813
$359$	−19.5732	−1.03303	−0.516516	−	0.856278i	$-0.672771\pi$
$359$	−19.5732	−1.03303	−0.516516	+	0.856278i	$0.672771\pi$
$360$	0.734387	0.0387056
$361$	25.7364	1.35455
$362$	4.86716	0.255812
$363$	6.06427	0.318292
$364$	−22.3043	−1.16906
$365$	5.07163	0.265461
$366$	−0.880705	−0.0460352
$367$	−1.78879	−0.0933743	−0.0466872	−	0.998910i	$-0.514866\pi$
$367$	−1.78879	−0.0933743	−0.0466872	+	0.998910i	$0.514866\pi$
$368$	0	0
$369$	−5.40047	−0.281137
$370$	−0.978264	−0.0508575
$371$	56.2637	2.92107
$372$	4.82928	0.250386
$373$	−0.688470	−0.0356476	−0.0178238	−	0.999841i	$-0.505674\pi$
$373$	−0.688470	−0.0356476	−0.0178238	+	0.999841i	$0.505674\pi$
$374$	−1.79036	−0.0925774
$375$	1.00000	0.0516398
$376$	1.66510	0.0858708
$377$	13.7703	0.709209
$378$	−0.775133	−0.0398686
$379$	−13.6084	−0.699016	−0.349508	−	0.936933i	$-0.613651\pi$
$379$	−13.6084	−0.699016	−0.349508	+	0.936933i	$0.613651\pi$
$380$	13.1477	0.674462
$381$	3.48413	0.178498
$382$	2.22262	0.113719
$383$	16.9222	0.864684	0.432342	−	0.901710i	$-0.357687\pi$
$383$	16.9222	0.864684	0.432342	+	0.901710i	$0.357687\pi$
$384$	5.67449	0.289575
$385$	−9.29924	−0.473933
$386$	−0.0658376	−0.00335105
$387$	10.6778	0.542783
$388$	2.08884	0.106045
$389$	−28.8328	−1.46188	−0.730940	−	0.682442i	$-0.760918\pi$
$389$	−28.8328	−1.46188	−0.730940	+	0.682442i	$0.760918\pi$
$390$	0.501998	0.0254197
$391$	0	0
$392$	−7.72604	−0.390224
$393$	−7.61728	−0.384241
$394$	2.60608	0.131292
$395$	9.20725	0.463267
$396$	−4.36711	−0.219456
$397$	−12.4043	−0.622555	−0.311278	−	0.950319i	$-0.600757\pi$
$397$	−12.4043	−0.622555	−0.311278	+	0.950319i	$0.600757\pi$
$398$	−4.07690	−0.204357
$399$	−27.9964	−1.40157
$400$	3.79542	0.189771
$401$	−30.2611	−1.51117	−0.755583	−	0.655052i	$-0.772647\pi$
$401$	−30.2611	−1.51117	−0.755583	+	0.655052i	$0.772647\pi$
$402$	−1.95488	−0.0975007
$403$	6.65980	0.331748
$404$	23.0735	1.14795
$405$	−1.00000	−0.0496904
$406$	3.93753	0.195416
$407$	11.7362	0.581741
$408$	−3.19585	−0.158218
$409$	24.1120	1.19226	0.596130	−	0.802888i	$-0.296704\pi$
$409$	24.1120	1.19226	0.596130	+	0.802888i	$0.296704\pi$
$410$	1.00008	0.0493906
$411$	19.1958	0.946859
$412$	−24.2254	−1.19350
$413$	25.5129	1.25541
$414$	0	0
$415$	8.87707	0.435758
$416$	5.88685	0.288626
$417$	5.85394	0.286669
$418$	2.75176	0.134593
$419$	29.7862	1.45515	0.727575	−	0.686028i	$-0.240647\pi$
$419$	29.7862	1.45515	0.727575	+	0.686028i	$0.240647\pi$
$420$	−8.22793	−0.401482
$421$	−16.8130	−0.819415	−0.409708	−	0.912217i	$-0.634369\pi$
$421$	−16.8130	−0.819415	−0.409708	+	0.912217i	$0.634369\pi$
$422$	1.03618	0.0504403
$423$	−2.26733	−0.110241
$424$	−9.87147	−0.479401
$425$	−4.35172	−0.211089
$426$	1.92266	0.0931530
$427$	19.9066	0.963350
$428$	11.7288	0.566935
$429$	−6.02245	−0.290766
$430$	−1.97736	−0.0953569
$431$	29.7647	1.43371	0.716857	−	0.697220i	$-0.245580\pi$
$431$	29.7647	1.43371	0.716857	+	0.697220i	$0.245580\pi$
$432$	−3.79542	−0.182607
$433$	13.8351	0.664875	0.332437	−	0.943125i	$-0.392129\pi$
$433$	13.8351	0.664875	0.332437	+	0.943125i	$0.392129\pi$
$434$	1.90432	0.0914103
$435$	5.07981	0.243558
$436$	5.57829	0.267152
$437$	0	0
$438$	0.939188	0.0448761
$439$	−8.51802	−0.406543	−0.203271	−	0.979122i	$-0.565157\pi$
$439$	−8.51802	−0.406543	−0.203271	+	0.979122i	$0.565157\pi$
$440$	1.63155	0.0777811
$441$	10.5204	0.500971
$442$	−2.18455	−0.103909
$443$	24.4951	1.16380	0.581898	−	0.813262i	$-0.302310\pi$
$443$	24.4951	1.16380	0.581898	+	0.813262i	$0.302310\pi$
$444$	10.3841	0.492809
$445$	−0.783796	−0.0371555
$446$	2.91815	0.138178
$447$	10.8501	0.513190
$448$	−30.0899	−1.42162
$449$	2.39958	0.113243	0.0566215	−	0.998396i	$-0.481967\pi$
$449$	2.39958	0.113243	0.0566215	+	0.998396i	$0.481967\pi$
$450$	0.185184	0.00872968
$451$	−11.9980	−0.564962
$452$	32.6408	1.53529
$453$	2.84135	0.133498
$454$	0.380392	0.0178527
$455$	−11.3467	−0.531941
$456$	4.91197	0.230024
$457$	−29.3642	−1.37360	−0.686799	−	0.726848i	$-0.740985\pi$
$457$	−29.3642	−1.37360	−0.686799	+	0.726848i	$0.740985\pi$
$458$	5.29318	0.247334
$459$	4.35172	0.203121
$460$	0	0
$461$	22.8083	1.06229	0.531144	−	0.847281i	$-0.321762\pi$
$461$	22.8083	1.06229	0.531144	+	0.847281i	$0.321762\pi$
$462$	−1.72207	−0.0801182
$463$	−27.5408	−1.27993	−0.639965	−	0.768404i	$-0.721051\pi$
$463$	−27.5408	−1.27993	−0.639965	+	0.768404i	$0.721051\pi$
$464$	19.2800	0.895051
$465$	2.45676	0.113930
$466$	−0.315157	−0.0145994
$467$	12.7824	0.591501	0.295750	−	0.955265i	$-0.404430\pi$
$467$	12.7824	0.591501	0.295750	+	0.955265i	$0.404430\pi$
$468$	−5.32864	−0.246316
$469$	44.1863	2.04034
$470$	0.419874	0.0193673
$471$	21.9832	1.01293
$472$	−4.47624	−0.206035
$473$	23.7223	1.09075
$474$	1.70504	0.0783150
$475$	6.68852	0.306891
$476$	35.8056	1.64115
$477$	13.4418	0.615456
$478$	2.56559	0.117348
$479$	−36.5879	−1.67174	−0.835872	−	0.548925i	$-0.815037\pi$
$479$	−36.5879	−1.67174	−0.835872	+	0.548925i	$0.815037\pi$
$480$	2.17163	0.0991207
$481$	14.3202	0.652945
$482$	−1.20379	−0.0548309
$483$	0	0
$484$	11.9206	0.541845
$485$	1.06264	0.0482520
$486$	−0.185184	−0.00840014
$487$	−26.4385	−1.19804	−0.599022	−	0.800732i	$-0.704444\pi$
$487$	−26.4385	−1.19804	−0.599022	+	0.800732i	$0.704444\pi$
$488$	−3.49262	−0.158103
$489$	0.0938907	0.00424588
$490$	−1.94821	−0.0880113
$491$	−36.9117	−1.66580	−0.832901	−	0.553421i	$-0.813322\pi$
$491$	−36.9117	−1.66580	−0.832901	+	0.553421i	$0.813322\pi$
$492$	−10.6157	−0.478595
$493$	−22.1059	−0.995600
$494$	3.35763	0.151067
$495$	−2.22165	−0.0998557
$496$	9.32444	0.418680
$497$	−43.4579	−1.94935
$498$	1.64389	0.0736647
$499$	16.5638	0.741496	0.370748	−	0.928733i	$-0.379101\pi$
$499$	16.5638	0.741496	0.370748	+	0.928733i	$0.379101\pi$
$500$	1.96571	0.0879091
$501$	−3.53996	−0.158154
$502$	2.07520	0.0926206
$503$	6.12304	0.273013	0.136506	−	0.990639i	$-0.456413\pi$
$503$	6.12304	0.273013	0.136506	+	0.990639i	$0.456413\pi$
$504$	−3.07395	−0.136925
$505$	11.7380	0.522335
$506$	0	0
$507$	5.65156	0.250995
$508$	6.84879	0.303866
$509$	−0.988946	−0.0438342	−0.0219171	−	0.999760i	$-0.506977\pi$
$509$	−0.988946	−0.0438342	−0.0219171	+	0.999760i	$0.506977\pi$
$510$	−0.805871	−0.0356846
$511$	−21.2285	−0.939095
$512$	13.8168	0.610624
$513$	−6.68852	−0.295306
$514$	3.78474	0.166938
$515$	−12.3240	−0.543062
$516$	20.9894	0.924008
$517$	−5.03721	−0.221536
$518$	4.09476	0.179913
$519$	−5.83761	−0.256243
$520$	1.99078	0.0873013
$521$	−31.4002	−1.37567	−0.687833	−	0.725869i	$-0.741438\pi$
$521$	−31.4002	−1.37567	−0.687833	+	0.725869i	$0.741438\pi$
$522$	0.940702	0.0411734
$523$	3.24854	0.142049	0.0710243	−	0.997475i	$-0.477373\pi$
$523$	3.24854	0.142049	0.0710243	+	0.997475i	$0.477373\pi$
$524$	−14.9733	−0.654114
$525$	−4.18574	−0.182681
$526$	5.20499	0.226948
$527$	−10.6912	−0.465714
$528$	−8.43208	−0.366959
$529$	0	0
$530$	−2.48921	−0.108124
$531$	6.09520	0.264509
$532$	−55.0327	−2.38597
$533$	−14.6396	−0.634111
$534$	−0.145147	−0.00628112
$535$	5.96673	0.257964
$536$	−7.75249	−0.334857
$537$	−24.9111	−1.07500
$538$	−2.41404	−0.104077
$539$	23.3726	1.00673
$540$	−1.96571	−0.0845905
$541$	24.7780	1.06529	0.532644	−	0.846339i	$-0.321198\pi$
$541$	24.7780	1.06529	0.532644	+	0.846339i	$0.321198\pi$
$542$	5.67013	0.243553
$543$	−26.2828	−1.12790
$544$	−9.45031	−0.405179
$545$	2.83780	0.121558
$546$	−2.10123	−0.0899244
$547$	9.26818	0.396279	0.198139	−	0.980174i	$-0.436510\pi$
$547$	9.26818	0.396279	0.198139	+	0.980174i	$0.436510\pi$
$548$	37.7333	1.61189
$549$	4.75583	0.202974
$550$	0.411415	0.0175428
$551$	33.9764	1.44744
$552$	0	0
$553$	−38.5391	−1.63885
$554$	−5.50696	−0.233968
$555$	5.28265	0.224236
$556$	11.5071	0.488011
$557$	−3.27144	−0.138615	−0.0693077	−	0.997595i	$-0.522079\pi$
$557$	−3.27144	−0.138615	−0.0693077	+	0.997595i	$0.522079\pi$
$558$	0.454955	0.0192598
$559$	28.9454	1.22426
$560$	−15.8866	−0.671332
$561$	9.66800	0.408183
$562$	−3.54014	−0.149332
$563$	23.9155	1.00792	0.503959	−	0.863727i	$-0.331876\pi$
$563$	23.9155	1.00792	0.503959	+	0.863727i	$0.331876\pi$
$564$	−4.45690	−0.187670
$565$	16.6051	0.698582
$566$	0.245187	0.0103060
$567$	4.18574	0.175784
$568$	7.62469	0.319925
$569$	14.4843	0.607213	0.303606	−	0.952798i	$-0.401809\pi$
$569$	14.4843	0.607213	0.303606	+	0.952798i	$0.401809\pi$
$570$	1.23861	0.0518797
$571$	21.4951	0.899542	0.449771	−	0.893144i	$-0.351506\pi$
$571$	21.4951	0.899542	0.449771	+	0.893144i	$0.351506\pi$
$572$	−11.8384	−0.494987
$573$	−12.0022	−0.501399
$574$	−4.18609	−0.174724
$575$	0	0
$576$	−7.18868	−0.299528
$577$	−11.9216	−0.496301	−0.248151	−	0.968721i	$-0.579823\pi$
$577$	−11.9216	−0.496301	−0.248151	+	0.968721i	$0.579823\pi$
$578$	0.358789	0.0149236
$579$	0.355524	0.0147751
$580$	9.98541	0.414622
$581$	−37.1571	−1.54153
$582$	0.196785	0.00815698
$583$	29.8629	1.23680
$584$	3.72454	0.154123
$585$	−2.71080	−0.112078
$586$	−0.605832	−0.0250267
$587$	−39.2517	−1.62009	−0.810046	−	0.586366i	$-0.800558\pi$
$587$	−39.2517	−1.62009	−0.810046	+	0.586366i	$0.800558\pi$
$588$	20.6800	0.852829
$589$	16.4321	0.677074
$590$	−1.12874	−0.0464693
$591$	−14.0729	−0.578881
$592$	20.0498	0.824044
$593$	29.4050	1.20752	0.603760	−	0.797166i	$-0.293668\pi$
$593$	29.4050	1.20752	0.603760	+	0.797166i	$0.293668\pi$
$594$	−0.411415	−0.0168806
$595$	18.2152	0.746748
$596$	21.3280	0.873630
$597$	22.0154	0.901029
$598$	0	0
$599$	13.7716	0.562692	0.281346	−	0.959606i	$-0.409219\pi$
$599$	13.7716	0.562692	0.281346	+	0.959606i	$0.409219\pi$
$600$	0.734387	0.0299812
$601$	−11.5091	−0.469467	−0.234733	−	0.972060i	$-0.575422\pi$
$601$	−11.5091	−0.469467	−0.234733	+	0.972060i	$0.575422\pi$
$602$	8.27672	0.337334
$603$	10.5564	0.429890
$604$	5.58527	0.227261
$605$	6.06427	0.246548
$606$	2.17370	0.0883004
$607$	−22.8264	−0.926497	−0.463248	−	0.886228i	$-0.653316\pi$
$607$	−22.8264	−0.926497	−0.463248	+	0.886228i	$0.653316\pi$
$608$	14.5250	0.589066
$609$	−21.2627	−0.861610
$610$	−0.880705	−0.0356587
$611$	−6.14628	−0.248652
$612$	8.55421	0.345783
$613$	24.6374	0.995094	0.497547	−	0.867437i	$-0.334234\pi$
$613$	24.6374	0.995094	0.497547	+	0.867437i	$0.334234\pi$
$614$	0.790837	0.0319156
$615$	−5.40047	−0.217768
$616$	−6.82924	−0.275158
$617$	7.19923	0.289830	0.144915	−	0.989444i	$-0.453709\pi$
$617$	7.19923	0.289830	0.144915	+	0.989444i	$0.453709\pi$
$618$	−2.28222	−0.0918043
$619$	−10.5065	−0.422292	−0.211146	−	0.977454i	$-0.567720\pi$
$619$	−10.5065	−0.422292	−0.211146	+	0.977454i	$0.567720\pi$
$620$	4.82928	0.193948
$621$	0	0
$622$	4.97776	0.199590
$623$	3.28076	0.131441
$624$	−10.2886	−0.411874
$625$	1.00000	0.0400000
$626$	3.05022	0.121911
$627$	−14.8596	−0.593434
$628$	43.2126	1.72437
$629$	−22.9886	−0.916616
$630$	−0.775133	−0.0308820
$631$	−8.05367	−0.320612	−0.160306	−	0.987067i	$-0.551248\pi$
$631$	−8.05367	−0.320612	−0.160306	+	0.987067i	$0.551248\pi$
$632$	6.76169	0.268965
$633$	−5.59537	−0.222396
$634$	1.82161	0.0723452
$635$	3.48413	0.138264
$636$	26.4226	1.04772
$637$	28.5187	1.12995
$638$	2.08991	0.0827403
$639$	−10.3824	−0.410721
$640$	5.67449	0.224304
$641$	−20.5779	−0.812779	−0.406389	−	0.913700i	$-0.633212\pi$
$641$	−20.5779	−0.812779	−0.406389	+	0.913700i	$0.633212\pi$
$642$	1.10495	0.0436088
$643$	−8.39805	−0.331187	−0.165593	−	0.986194i	$-0.552954\pi$
$643$	−8.39805	−0.331187	−0.165593	+	0.986194i	$0.552954\pi$
$644$	0	0
$645$	10.6778	0.420438
$646$	−5.39009	−0.212070
$647$	41.0424	1.61354	0.806771	−	0.590865i	$-0.201213\pi$
$647$	41.0424	1.61354	0.806771	+	0.590865i	$0.201213\pi$
$648$	−0.734387	−0.0288495
$649$	13.5414	0.531546
$650$	0.501998	0.0196900
$651$	−10.2834	−0.403037
$652$	0.184562	0.00722799
$653$	−4.29728	−0.168166	−0.0840829	−	0.996459i	$-0.526796\pi$
$653$	−4.29728	−0.168166	−0.0840829	+	0.996459i	$0.526796\pi$
$654$	0.525517	0.0205494
$655$	−7.61728	−0.297632
$656$	−20.4970	−0.800275
$657$	−5.07163	−0.197863
$658$	−1.75748	−0.0685138
$659$	4.55539	0.177453	0.0887263	−	0.996056i	$-0.471720\pi$
$659$	4.55539	0.177453	0.0887263	+	0.996056i	$0.471720\pi$
$660$	−4.36711	−0.169990
$661$	−42.7688	−1.66351	−0.831757	−	0.555140i	$-0.812665\pi$
$661$	−42.7688	−1.66351	−0.831757	+	0.555140i	$0.812665\pi$
$662$	−0.807545	−0.0313861
$663$	11.7966	0.458144
$664$	6.51920	0.252994
$665$	−27.9964	−1.08565
$666$	0.978264	0.0379070
$667$	0	0
$668$	−6.95852	−0.269233
$669$	−15.7581	−0.609242
$670$	−1.95488	−0.0755237
$671$	10.5658	0.407888
$672$	−9.08986	−0.350649
$673$	1.29195	0.0498009	0.0249004	−	0.999690i	$-0.492073\pi$
$673$	1.29195	0.0498009	0.0249004	+	0.999690i	$0.492073\pi$
$674$	−2.14768	−0.0827256
$675$	−1.00000	−0.0384900
$676$	11.1093	0.427281
$677$	−23.9672	−0.921134	−0.460567	−	0.887625i	$-0.652354\pi$
$677$	−23.9672	−0.921134	−0.460567	+	0.887625i	$0.652354\pi$
$678$	3.07501	0.118095
$679$	−4.44793	−0.170696
$680$	−3.19585	−0.122555
$681$	−2.05413	−0.0787143
$682$	1.01075	0.0387036
$683$	38.1569	1.46003	0.730017	−	0.683429i	$-0.239512\pi$
$683$	38.1569	1.46003	0.730017	+	0.683429i	$0.239512\pi$
$684$	−13.1477	−0.502714
$685$	19.1958	0.733434
$686$	2.72877	0.104185
$687$	−28.5833	−1.09052
$688$	40.5267	1.54507
$689$	36.4380	1.38818
$690$	0	0
$691$	−14.9028	−0.566930	−0.283465	−	0.958983i	$-0.591484\pi$
$691$	−14.9028	−0.566930	−0.283465	+	0.958983i	$0.591484\pi$
$692$	−11.4750	−0.436215
$693$	9.29924	0.353249
$694$	−3.69222	−0.140155
$695$	5.85394	0.222053
$696$	3.73055	0.141406
$697$	23.5013	0.890177
$698$	−2.94221	−0.111364
$699$	1.70186	0.0643701
$700$	−8.22793	−0.310987
$701$	−2.26631	−0.0855972	−0.0427986	−	0.999084i	$-0.513627\pi$
$701$	−2.26631	−0.0855972	−0.0427986	+	0.999084i	$0.513627\pi$
$702$	−0.501998	−0.0189467
$703$	35.3331	1.33261
$704$	−15.9707	−0.601920
$705$	−2.26733	−0.0853925
$706$	3.62978	0.136609
$707$	−49.1322	−1.84781
$708$	11.9814	0.450288
$709$	−43.8610	−1.64723	−0.823616	−	0.567147i	$-0.808047\pi$
$709$	−43.8610	−1.64723	−0.823616	+	0.567147i	$0.808047\pi$
$710$	1.92266	0.0721560
$711$	−9.20725	−0.345299
$712$	−0.575610	−0.0215719
$713$	0	0
$714$	3.37316	0.126237
$715$	−6.02245	−0.225227
$716$	−48.9680	−1.83002
$717$	−13.8543	−0.517397
$718$	−3.62464	−0.135271
$719$	22.2025	0.828012	0.414006	−	0.910274i	$-0.364129\pi$
$719$	22.2025	0.828012	0.414006	+	0.910274i	$0.364129\pi$
$720$	−3.79542	−0.141447
$721$	51.5852	1.92113
$722$	4.76597	0.177371
$723$	6.50047	0.241755
$724$	−51.6643	−1.92009
$725$	5.07981	0.188659
$726$	1.12301	0.0416788
$727$	1.68112	0.0623494	0.0311747	−	0.999514i	$-0.490075\pi$
$727$	1.68112	0.0623494	0.0311747	+	0.999514i	$0.490075\pi$
$728$	−8.33287	−0.308837
$729$	1.00000	0.0370370
$730$	0.939188	0.0347609
$731$	−46.4668	−1.71864
$732$	9.34856	0.345533
$733$	−16.5826	−0.612491	−0.306245	−	0.951953i	$-0.599073\pi$
$733$	−16.5826	−0.612491	−0.306245	+	0.951953i	$0.599073\pi$
$734$	−0.331257	−0.0122269
$735$	10.5204	0.388050
$736$	0	0
$737$	23.4526	0.863889
$738$	−1.00008	−0.0368136
$739$	6.51904	0.239807	0.119903	−	0.992786i	$-0.461742\pi$
$739$	6.51904	0.239807	0.119903	+	0.992786i	$0.461742\pi$
$740$	10.3841	0.381728
$741$	−18.1313	−0.666068
$742$	10.4192	0.382500
$743$	14.2148	0.521492	0.260746	−	0.965407i	$-0.416032\pi$
$743$	14.2148	0.521492	0.260746	+	0.965407i	$0.416032\pi$
$744$	1.80422	0.0661458
$745$	10.8501	0.397515
$746$	−0.127494	−0.00466788
$747$	−8.87707	−0.324795
$748$	19.0044	0.694871
$749$	−24.9752	−0.912573
$750$	0.185184	0.00676198
$751$	−7.14155	−0.260599	−0.130299	−	0.991475i	$-0.541594\pi$
$751$	−7.14155	−0.260599	−0.130299	+	0.991475i	$0.541594\pi$
$752$	−8.60546	−0.313809
$753$	−11.2061	−0.408373
$754$	2.55005	0.0928675
$755$	2.84135	0.103407
$756$	8.22793	0.299247
$757$	10.3054	0.374557	0.187278	−	0.982307i	$-0.440033\pi$
$757$	10.3054	0.374557	0.187278	+	0.982307i	$0.440033\pi$
$758$	−2.52006	−0.0915328
$759$	0	0
$760$	4.91197	0.178176
$761$	−8.93250	−0.323803	−0.161901	−	0.986807i	$-0.551763\pi$
$761$	−8.93250	−0.323803	−0.161901	+	0.986807i	$0.551763\pi$
$762$	0.645208	0.0233734
$763$	−11.8783	−0.430023
$764$	−23.5928	−0.853557
$765$	4.35172	0.157337
$766$	3.13373	0.113226
$767$	16.5229	0.596606
$768$	−13.3265	−0.480880
$769$	−27.9326	−1.00728	−0.503638	−	0.863915i	$-0.668005\pi$
$769$	−27.9326	−1.00728	−0.503638	+	0.863915i	$0.668005\pi$
$770$	−1.72207	−0.0620593
$771$	−20.4377	−0.736044
$772$	0.698857	0.0251524
$773$	47.5627	1.71071	0.855355	−	0.518042i	$-0.173339\pi$
$773$	47.5627	1.71071	0.855355	+	0.518042i	$0.173339\pi$
$774$	1.97736	0.0710748
$775$	2.45676	0.0882496
$776$	0.780390	0.0280144
$777$	−22.1118	−0.793255
$778$	−5.33938	−0.191426
$779$	−36.1212	−1.29418
$780$	−5.32864	−0.190796
$781$	−23.0660	−0.825367
$782$	0	0
$783$	−5.07981	−0.181538
$784$	39.9293	1.42604
$785$	21.9832	0.784615
$786$	−1.41060	−0.0503145
$787$	24.8019	0.884094	0.442047	−	0.896992i	$-0.354253\pi$
$787$	24.8019	0.884094	0.442047	+	0.896992i	$0.354253\pi$
$788$	−27.6632	−0.985459
$789$	−28.1070	−1.00064
$790$	1.70504	0.0606626
$791$	−69.5046	−2.47130
$792$	−1.63155	−0.0579746
$793$	12.8921	0.457812
$794$	−2.29709	−0.0815206
$795$	13.4418	0.476731
$796$	43.2758	1.53387
$797$	11.0885	0.392774	0.196387	−	0.980526i	$-0.437079\pi$
$797$	11.0885	0.392774	0.196387	+	0.980526i	$0.437079\pi$
$798$	−5.18450	−0.183529
$799$	9.86678	0.349062
$800$	2.17163	0.0767786
$801$	0.783796	0.0276941
$802$	−5.60388	−0.197880
$803$	−11.2674	−0.397618
$804$	20.7508	0.731824
$805$	0	0
$806$	1.23329	0.0434408
$807$	13.0359	0.458885
$808$	8.62024	0.303259
$809$	9.85381	0.346441	0.173221	−	0.984883i	$-0.444583\pi$
$809$	9.85381	0.346441	0.173221	+	0.984883i	$0.444583\pi$
$810$	−0.185184	−0.00650672
$811$	38.0433	1.33588	0.667940	−	0.744215i	$-0.267176\pi$
$811$	38.0433	1.33588	0.667940	+	0.744215i	$0.267176\pi$
$812$	−41.7963	−1.46676
$813$	−30.6188	−1.07385
$814$	2.17336	0.0761762
$815$	0.0938907	0.00328885
$816$	16.5166	0.578196
$817$	71.4187	2.49862
$818$	4.46516	0.156121
$819$	11.3467	0.396486
$820$	−10.6157	−0.370718
$821$	4.86915	0.169934	0.0849672	−	0.996384i	$-0.472921\pi$
$821$	4.86915	0.169934	0.0849672	+	0.996384i	$0.472921\pi$
$822$	3.55476	0.123987
$823$	38.0462	1.32621	0.663103	−	0.748528i	$-0.269239\pi$
$823$	38.0462	1.32621	0.663103	+	0.748528i	$0.269239\pi$
$824$	−9.05061	−0.315293
$825$	−2.22165	−0.0773479
$826$	4.72459	0.164390
$827$	−2.57032	−0.0893787	−0.0446893	−	0.999001i	$-0.514230\pi$
$827$	−2.57032	−0.0893787	−0.0446893	+	0.999001i	$0.514230\pi$
$828$	0	0
$829$	42.3456	1.47072	0.735362	−	0.677674i	$-0.237012\pi$
$829$	42.3456	1.47072	0.735362	+	0.677674i	$0.237012\pi$
$830$	1.64389	0.0570604
$831$	29.7377	1.03159
$832$	−19.4871	−0.675593
$833$	−45.7818	−1.58624
$834$	1.08406	0.0375379
$835$	−3.53996	−0.122505
$836$	−29.2095	−1.01023
$837$	−2.45676	−0.0849182
$838$	5.51594	0.190545
$839$	−21.9907	−0.759204	−0.379602	−	0.925150i	$-0.623939\pi$
$839$	−21.9907	−0.759204	−0.379602	+	0.925150i	$0.623939\pi$
$840$	−3.07395	−0.106061
$841$	−3.19554	−0.110191
$842$	−3.11350	−0.107298
$843$	19.1168	0.658419
$844$	−10.9989	−0.378597
$845$	5.65156	0.194420
$846$	−0.419874	−0.0144356
$847$	−25.3835	−0.872186
$848$	51.0171	1.75194
$849$	−1.32401	−0.0454401
$850$	−0.805871	−0.0276411
$851$	0	0
$852$	−20.4087	−0.699191
$853$	−13.0377	−0.446402	−0.223201	−	0.974772i	$-0.571651\pi$
$853$	−13.0377	−0.446402	−0.223201	+	0.974772i	$0.571651\pi$
$854$	3.68640	0.126146
$855$	−6.68852	−0.228743
$856$	4.38189	0.149770
$857$	8.09087	0.276379	0.138189	−	0.990406i	$-0.455872\pi$
$857$	8.09087	0.276379	0.138189	+	0.990406i	$0.455872\pi$
$858$	−1.11526	−0.0380745
$859$	26.5397	0.905523	0.452761	−	0.891632i	$-0.350439\pi$
$859$	26.5397	0.905523	0.452761	+	0.891632i	$0.350439\pi$
$860$	20.9894	0.715733
$861$	22.6050	0.770375
$862$	5.51196	0.187738
$863$	26.2183	0.892480	0.446240	−	0.894913i	$-0.352763\pi$
$863$	26.2183	0.892480	0.446240	+	0.894913i	$0.352763\pi$
$864$	−2.17163	−0.0738802
$865$	−5.83761	−0.198485
$866$	2.56205	0.0870621
$867$	−1.93747	−0.0657998
$868$	−20.2141	−0.686111
$869$	−20.4553	−0.693898
$870$	0.940702	0.0318928
$871$	28.6163	0.969627
$872$	2.08405	0.0705748
$873$	−1.06264	−0.0359649
$874$	0	0
$875$	−4.18574	−0.141504
$876$	−9.96934	−0.336833
$877$	36.3858	1.22866	0.614330	−	0.789049i	$-0.289426\pi$
$877$	36.3858	1.22866	0.614330	+	0.789049i	$0.289426\pi$
$878$	−1.57740	−0.0532348
$879$	3.27151	0.110345
$880$	−8.43208	−0.284246
$881$	7.66233	0.258150	0.129075	−	0.991635i	$-0.458799\pi$
$881$	7.66233	0.258150	0.129075	+	0.991635i	$0.458799\pi$
$882$	1.94821	0.0655997
$883$	−28.9939	−0.975723	−0.487861	−	0.872921i	$-0.662223\pi$
$883$	−28.9939	−0.975723	−0.487861	+	0.872921i	$0.662223\pi$
$884$	23.1887	0.779922
$885$	6.09520	0.204888
$886$	4.53611	0.152394
$887$	−32.2648	−1.08335	−0.541674	−	0.840589i	$-0.682209\pi$
$887$	−32.2648	−1.08335	−0.541674	+	0.840589i	$0.682209\pi$
$888$	3.87951	0.130188
$889$	−14.5837	−0.489121
$890$	−0.145147	−0.00486533
$891$	2.22165	0.0744281
$892$	−30.9757	−1.03714
$893$	−15.1651	−0.507480
$894$	2.00926	0.0671998
$895$	−24.9111	−0.832688
$896$	−23.7519	−0.793495
$897$	0	0
$898$	0.444364	0.0148286
$899$	12.4799	0.416228
$900$	−1.96571	−0.0655236
$901$	−58.4948	−1.94875
$902$	−2.22183	−0.0739790
$903$	−44.6944	−1.48734
$904$	12.1946	0.405586
$905$	−26.2828	−0.873670
$906$	0.526174	0.0174810
$907$	−48.1780	−1.59972	−0.799862	−	0.600184i	$-0.795094\pi$
$907$	−48.1780	−1.59972	−0.799862	+	0.600184i	$0.795094\pi$
$908$	−4.03781	−0.133999
$909$	−11.7380	−0.389325
$910$	−2.10123	−0.0696551
$911$	−35.5630	−1.17826	−0.589128	−	0.808040i	$-0.700529\pi$
$911$	−35.5630	−1.17826	−0.589128	+	0.808040i	$0.700529\pi$
$912$	−25.3857	−0.840606
$913$	−19.7217	−0.652694
$914$	−5.43778	−0.179866
$915$	4.75583	0.157223
$916$	−56.1863	−1.85645
$917$	31.8839	1.05290
$918$	0.805871	0.0265977
$919$	−58.6491	−1.93465	−0.967327	−	0.253532i	$-0.918408\pi$
$919$	−58.6491	−1.93465	−0.967327	+	0.253532i	$0.918408\pi$
$920$	0	0
$921$	−4.27054	−0.140719
$922$	4.22374	0.139102
$923$	−28.1446	−0.926389
$924$	18.2796	0.601354
$925$	5.28265	0.173692
$926$	−5.10013	−0.167601
$927$	12.3240	0.404774
$928$	11.0314	0.362125
$929$	−7.18750	−0.235814	−0.117907	−	0.993025i	$-0.537618\pi$
$929$	−7.18750	−0.235814	−0.117907	+	0.993025i	$0.537618\pi$
$930$	0.454955	0.0149185
$931$	70.3659	2.30615
$932$	3.34535	0.109581
$933$	−26.8800	−0.880012
$934$	2.36711	0.0774542
$935$	9.66800	0.316177
$936$	−1.99078	−0.0650706
$937$	15.6013	0.509671	0.254835	−	0.966984i	$-0.417979\pi$
$937$	15.6013	0.509671	0.254835	+	0.966984i	$0.417979\pi$
$938$	8.18262	0.267172
$939$	−16.4712	−0.537519
$940$	−4.45690	−0.145368
$941$	36.6900	1.19606	0.598030	−	0.801474i	$-0.295950\pi$
$941$	36.6900	1.19606	0.598030	+	0.801474i	$0.295950\pi$
$942$	4.07095	0.132639
$943$	0	0
$944$	23.1338	0.752942
$945$	4.18574	0.136162
$946$	4.39301	0.142829
$947$	−55.0681	−1.78947	−0.894737	−	0.446594i	$-0.852637\pi$
$947$	−55.0681	−1.78947	−0.894737	+	0.446594i	$0.852637\pi$
$948$	−18.0987	−0.587820
$949$	−13.7482	−0.446285
$950$	1.23861	0.0401858
$951$	−9.83672	−0.318977
$952$	13.3770	0.433550
$953$	18.1389	0.587576	0.293788	−	0.955871i	$-0.405084\pi$
$953$	18.1389	0.587576	0.293788	+	0.955871i	$0.405084\pi$
$954$	2.48921	0.0805911
$955$	−12.0022	−0.388382
$956$	−27.2334	−0.880792
$957$	−11.2856	−0.364810
$958$	−6.77551	−0.218907
$959$	−80.3485	−2.59459
$960$	−7.18868	−0.232014
$961$	−24.9643	−0.805300
$962$	2.65188	0.0855000
$963$	−5.96673	−0.192275
$964$	12.7780	0.411552
$965$	0.355524	0.0114447
$966$	0	0
$967$	37.8260	1.21640	0.608201	−	0.793783i	$-0.291892\pi$
$967$	37.8260	1.21640	0.608201	+	0.793783i	$0.291892\pi$
$968$	4.45352	0.143142
$969$	29.1066	0.935038
$970$	0.196785	0.00631837
$971$	−6.49918	−0.208569	−0.104284	−	0.994548i	$-0.533255\pi$
$971$	−6.49918	−0.208569	−0.104284	+	0.994548i	$0.533255\pi$
$972$	1.96571	0.0630501
$973$	−24.5031	−0.785532
$974$	−4.89601	−0.156878
$975$	−2.71080	−0.0868151
$976$	18.0503	0.577778
$977$	34.0867	1.09053	0.545264	−	0.838264i	$-0.316429\pi$
$977$	34.0867	1.09053	0.545264	+	0.838264i	$0.316429\pi$
$978$	0.0173871	0.000555978 0
$979$	1.74132	0.0556528
$980$	20.6800	0.660598
$981$	−2.83780	−0.0906041
$982$	−6.83548	−0.218129
$983$	61.2968	1.95506	0.977532	−	0.210785i	$-0.0676020\pi$
$983$	61.2968	1.95506	0.977532	+	0.210785i	$0.0676020\pi$
$984$	−3.96604	−0.126433
$985$	−14.0729	−0.448399
$986$	−4.09367	−0.130369
$987$	9.49044	0.302084
$988$	−35.6407	−1.13388
$989$	0	0
$990$	−0.411415	−0.0130756
$991$	8.77523	0.278754	0.139377	−	0.990239i	$-0.455490\pi$
$991$	8.77523	0.278754	0.139377	+	0.990239i	$0.455490\pi$
$992$	5.33517	0.169392
$993$	4.36076	0.138384
$994$	−8.04773	−0.255258
$995$	22.0154	0.697934
$996$	−17.4497	−0.552915
$997$	62.0467	1.96504	0.982519	−	0.186161i	$-0.0596046\pi$
$997$	62.0467	1.96504	0.982519	+	0.186161i	$0.0596046\pi$
$998$	3.06735	0.0970954
$999$	−5.28265	−0.167136

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bt.1.14		25
23.11	odd	22		345.2.m.d.121.3	✓	50
23.21	odd	22		345.2.m.d.211.3	yes	50
23.22	odd	2		7935.2.a.bu.1.14		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.121.3	✓	50	23.11	odd	22
345.2.m.d.211.3	yes	50	23.21	odd	22
7935.2.a.bt.1.14		25	1.1	even	1	trivial
7935.2.a.bu.1.14		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.185184 q^{2} -1.00000 q^{3} -1.96571 q^{4} -1.00000 q^{5} -0.185184 q^{6} +4.18574 q^{7} -0.734387 q^{8} +1.00000 q^{9} -0.185184 q^{10} +2.22165 q^{11} +1.96571 q^{12} +2.71080 q^{13} +0.775133 q^{14} +1.00000 q^{15} +3.79542 q^{16} -4.35172 q^{17} +0.185184 q^{18} +6.68852 q^{19} +1.96571 q^{20} -4.18574 q^{21} +0.411415 q^{22} +0.734387 q^{24} +1.00000 q^{25} +0.501998 q^{26} -1.00000 q^{27} -8.22793 q^{28} +5.07981 q^{29} +0.185184 q^{30} +2.45676 q^{31} +2.17163 q^{32} -2.22165 q^{33} -0.805871 q^{34} -4.18574 q^{35} -1.96571 q^{36} +5.28265 q^{37} +1.23861 q^{38} -2.71080 q^{39} +0.734387 q^{40} -5.40047 q^{41} -0.775133 q^{42} +10.6778 q^{43} -4.36711 q^{44} -1.00000 q^{45} -2.26733 q^{47} -3.79542 q^{48} +10.5204 q^{49} +0.185184 q^{50} +4.35172 q^{51} -5.32864 q^{52} +13.4418 q^{53} -0.185184 q^{54} -2.22165 q^{55} -3.07395 q^{56} -6.68852 q^{57} +0.940702 q^{58} +6.09520 q^{59} -1.96571 q^{60} +4.75583 q^{61} +0.454955 q^{62} +4.18574 q^{63} -7.18868 q^{64} -2.71080 q^{65} -0.411415 q^{66} +10.5564 q^{67} +8.55421 q^{68} -0.775133 q^{70} -10.3824 q^{71} -0.734387 q^{72} -5.07163 q^{73} +0.978264 q^{74} -1.00000 q^{75} -13.1477 q^{76} +9.29924 q^{77} -0.501998 q^{78} -9.20725 q^{79} -3.79542 q^{80} +1.00000 q^{81} -1.00008 q^{82} -8.87707 q^{83} +8.22793 q^{84} +4.35172 q^{85} +1.97736 q^{86} -5.07981 q^{87} -1.63155 q^{88} +0.783796 q^{89} -0.185184 q^{90} +11.3467 q^{91} -2.45676 q^{93} -0.419874 q^{94} -6.68852 q^{95} -2.17163 q^{96} -1.06264 q^{97} +1.94821 q^{98} +2.22165 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 - 25 * q^5 - q^6 + 15 * q^7 + 3 * q^8 + 25 * q^9 - q^10 - 15 * q^11 - 31 * q^12 + 24 * q^13 - 5 * q^14 + 25 * q^15 + 39 * q^16 + 6 * q^17 + q^18 - 13 * q^19 - 31 * q^20 - 15 * q^21 + 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 + 41 * q^28 + q^29 + q^30 + 18 * q^31 + 17 * q^32 + 15 * q^33 - 7 * q^34 - 15 * q^35 + 31 * q^36 + 8 * q^37 - 15 * q^38 - 24 * q^39 - 3 * q^40 + 36 * q^41 + 5 * q^42 + 36 * q^43 - 90 * q^44 - 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 - 6 * q^51 + 35 * q^52 - 6 * q^53 - q^54 + 15 * q^55 - 15 * q^56 + 13 * q^57 + 42 * q^58 - 3 * q^59 + 31 * q^60 - 71 * q^61 - 7 * q^62 + 15 * q^63 + 47 * q^64 - 24 * q^65 - 21 * q^66 + 10 * q^67 + 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 - 67 * q^74 - 25 * q^75 + 12 * q^76 + 27 * q^77 - 21 * q^78 - 33 * q^79 - 39 * q^80 + 25 * q^81 + 49 * q^82 + 2 * q^83 - 41 * q^84 - 6 * q^85 + 35 * q^86 - q^87 + 33 * q^88 - 11 * q^89 - q^90 - 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 + 48 * q^97 + 4 * q^98 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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